Simplify the following expression: $n = \dfrac{7p^2 - 21p - 28}{p + 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ n =\dfrac{7(p^2 - 3p - 4)}{p + 1} $ Then we factor the remaining polynomial: $p^2 {-3}p {-4} $ ${1} {-4} = {-3}$ ${1} \times {-4} = {-4}$ $ (p + {1}) (p {-4}) $ This gives us a factored expression: $\dfrac{7(p + {1}) (p {-4})}{p + 1}$ We can divide the numerator and denominator by $(p - 1)$ on condition that $p \neq -1$ Therefore $n = 7(p - 4); p \neq -1$